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arXiv · 1111.2614

Nucleon axial and pseudoscalar form factors from the covariant Faddeev equation

Gernot Eichmann·Christian S. Fischer
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Abstract

We compute the axial and pseudoscalar form factors of the nucleon in the Dyson-Schwinger approach. To this end, we solve a covariant three-body Faddeev equation for the nucleon wave function and determine the matrix elements of the axialvector and pseudoscalar isotriplet currents. Our only input is a well-established and phenomenologically successful ansatz for the nonperturbative quark-gluon interaction. As a consequence of the axial Ward-Takahashi identity that is respected at the quark level, the Goldberger-Treiman relation is reproduced for all current-quark masses. We discuss the timelike pole structure of the quark-antiquark vertices that enters the nucleon matrix elements and determines the momentum dependence of the form factors. Our result for the axial charge underestimates the experimental value by 20-25% which might be a signal of missing pion-cloud contributions. The axial and pseudoscalar form factors agree with phenomenological and lattice data in the momentum range above Q^2 ~ 1...2 GeV^2.

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Gernot Eichmann, Christian S. Fischer. 2011-11-10. Nucleon axial and pseudoscalar form factors from the covariant Faddeev equation. https://doi.org/10.1140/epja/i2012-12009-6

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